نتایج جستجو برای: jacobson radical
تعداد نتایج: 92985 فیلتر نتایج به سال:
Jacobson argues that our statement that "many climate models may overestimate warming by BC" has not been demonstrated. Jacobson challenges our results on the basis that we have misinterpreted some model results, omitted optical focusing under high relative humidity conditions and by involatile components, and because our measurements consist of only two locations over short atmospheric time pe...
Let R be a ring and R a self-orthogonal module. We introduce the notion of the right orthogonal dimension (relative to R ) of modules. We give a criterion for computing this relative right orthogonal dimension of modules. For a left coherent and semilocal ring R and a finitely presented self-orthogonal module R , we show that the projective dimension of R and the right orthogonal dimension (rel...
1. Amitsur in his paper on Finite Dimensional Central Division Algebras [l] has proved that in a division ring D with center C, (P: C) 5= ra2 < =o if and only if every primitive homomorphic image of a polynomial ring P[x] is a complete matrix ring Ah, h^n, over a division ring A. Equivalently speaking, a division ring is finite dimensional over its center if and only if the polynomial ring over...
We develop the theory of “branch algebras”, which are infinitedimensional associative algebras that are isomorphic, up to taking subrings of finite codimension, to a matrix ring over themselves. The main examples come from groups acting on trees. In particular, for every field k we construct a k-algebra K which • is finitely generated and infinite-dimensional, but has only finite-dimensional qu...
Exponent matrices appeared in the study of tiled orders over discrete valuation rings. Many properties of such orders are formulated using this notion. We think that such matrices are of interest in them own right, in particular, it is convenient to write finite partially ordered sets (posets) and finite metric spaces as special exponent matrices. Note that when we defined a quiver Q(E) of a re...
A right ideal A of a ring R is called annihilator-small if A+ T = R; T a right ideal, implies that l(T ) = 0; where l( ) indicates the left annihilator. The sum Ar of all such right ideals turns out to be a two-sided ideal that contains the Jacobson radical and the left singular ideal, and is contained in the ideal generated by the total of the ring. The ideal Ar is studied, conditions when it ...
We prove that in a ring Rwith an identity there exists an element a ∈ R and a nonzero derivation d ∈ Der R such that ad(a) 6= 0. A ring R is said to be a d-rigid ring for some derivation d ∈ Der R if d(a) = 0 or ad(a) 6= 0 for all a ∈ R. We study rings with rigid derivations and establish that a commutative Artinian ring R either has a non-rigid derivation or R = R1 ⊕ · · · ⊕ Rn is a ring direc...
We give a criterion for when idempotents of a ring R which commute modulo the Jacobson radical J(R) can be lifted to commuting idempotents of R. If such lifting is possible, we give extra information about the lifts. A “half-commuting” analogue is also proven, and this is used to give sufficient conditions for a ring to have the internal exchange property. In particular, we show that if R/J(R) ...
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